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What does duality really mean?
Author(s) -
Iri Masao,
Recski András
Publication year - 1980
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490080311
Subject(s) - matroid , reciprocal , nobody , duality (order theory) , phenomenon , mathematics , homogeneous space , graph theory , mathematical economics , computer science , calculus (dental) , discrete mathematics , epistemology , combinatorics , philosophy , linguistics , medicine , geometry , dentistry , operating system
The average network theorist answers this question by speaking about the interchange of the roles of voltage and current, while the average mathematician uses orthogonal vector spaces for his definition (as in mathematical programming, matroid theory, etc.). What is even worse, both of them believe that the two definitions are essentially the same. The main aim of the present paper is to show that this is the case for reciprocal networks only. Hence, in the theory of non‐reciprocal networks, two entirely different voltage‐current symmetries exist . We also show that both concepts are naturally related to the same, well known, duality principle of graph theory which also explains why nobody seems to have observed this phenomenon till now.